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3-brilliant numbers with distinct prime factors.
1

%I #16 Oct 12 2024 14:43:53

%S 30,42,70,105,2431,2717,3289,3553,4147,4199,4301,4433,4807,5083,5291,

%T 5423,5681,5797,5863,6061,6149,6409,6479,6721,6851,6919,7163,7337,

%U 7429,7579,7657,7667,7733,7843,8041,8177,8437,8569,8671,8723,8789,8987,9061,9139,9269

%N 3-brilliant numbers with distinct prime factors.

%H Michael S. Branicky, <a href="/A376800/b376800.txt">Table of n, a(n) for n = 1..10000</a>

%e 30 = 2*3*5 is a term.

%e 2431 = 11*13*17 is a term.

%o (Python)

%o from sympy import factorint

%o def ok(n):

%o f = factorint(n)

%o return len(f) == sum(f.values()) == 3 and len(set([len(str(p)) for p in f])) == 1

%o print([k for k in range(9300) if ok(k)]) # _Michael S. Branicky_, Oct 05 2024

%o (Python)

%o from math import prod

%o from sympy import primerange

%o from itertools import count, combinations, islice

%o def bgen(d): # generator of terms that are products of d-digit primes

%o primes, out = list(primerange(10**(d-1), 10**d)), set()

%o for t in combinations(primes, 3): out.add(prod(t))

%o yield from sorted(out)

%o def agen(): # generator of terms

%o for d in count(1): yield from bgen(d)

%o print(list(islice(agen(), 45))) # _Michael S. Branicky_, Oct 05 2024

%Y Intersection of A376703 and A007304.

%K nonn,base,easy

%O 1,1

%A _Paul Duckett_, Oct 04 2024

%E a(6) and beyond from _Michael S. Branicky_, Oct 05 2024